Changing dimensions of a Child
Revised per chat conversation to get down to the real problem.

The problem at its root had to do with a parent object relationship, and the sphere subordinate to this parent object was parented without the 'KEEP TRANSFORM' option. when this happens, the values begin to change in the scale of the subordinate, then the parent calculates what the subordinate should be and the subordinate changes its scale value automatically to adjust. So it became pretty unstable to adjust the values in the subordinate object.

To fix the root of the problem, we cleared the parent (Alt+P), then reparented the subordinate back to its original parent (via Ctrl+P >> Then clicked the 'Parent (keep transform)' option).

Then the rest of these steps worked in this scenario...




Change the dimensions to all be at full scale (12.756, 12.756, 12.756).
Then Apply the scale.
Then change your scale on X to 12.720/12.7560000000.




Appended per comments below:



(desired size) / (original size + 'appended zeros to go to the 10th decimal'), ENTER